Abstract
We prepare and study a two-component Mott insulator of bosonic atoms with two particles per site. The mapping of this system to a magnetic spin model, and the subsequent study of its quantum phases, require a detailed knowledge of the interaction strengths of the two components. In this work, we use radio frequency (RF) transitions and an on-site interaction blockade for precise, empirical determination of the interaction strengths of different combinations of hyperfine states on a single lattice site. We create a map of the interactions of the lowest two hyperfine states of $^7$Li as a function of magnetic field, including measurements of several Feshbach resonances with unprecedented sensitivity, and we identify promising regions for the realization of magnetic spin models.
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